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49
Constraint propagation
- Handbook of Constraint Programming
, 2006
"... Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent ..."
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Cited by 76 (5 self)
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Constraint propagation is a form of inference, not search, and as such is more ”satisfying”, both technically and aesthetically. —E.C. Freuder, 2005. Constraint reasoning involves various types of techniques to tackle the inherent
Domain Filtering Consistencies
- Journal of Artificial Intelligence Research (JAIR)
, 2001
"... Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been kn ..."
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Cited by 72 (8 self)
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Enforcing local consistencies is one of the main features of constraint reasoning. Which level of local consistency should be used when searching for solutions in a constraint network is a basic question. Arc consistency and partial forms of arc consistency have been widely studied, and have been known for sometime through the forward checking or the MAC search algorithms. Until recently, stronger forms of local consistency remained limited to those that change the structure of the constraint graph, and thus, could not be used in practice, especially on large networks. This paper focuses on the local consistencies that are stronger than arc consistency, without changing the structure of the network, i.e., only removing inconsistent values from the domains. In the last five years, several such local consistencies have been proposed by us or by others. We make an overview of all of them, and highlight some relations between them. We compare them both theoretically and experimentally, considering their pruning efficiency and the time required to enforce them.
Encodings of Non-Binary Constraint Satisfaction Problems
, 1999
"... We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of non-binary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. ..."
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Cited by 47 (10 self)
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We perform a detailed theoretical and empirical comparison of the dual and hidden variable encodings of non-binary constraint satisfaction problems. We identify a simple relationship between the two encodings by showing how we can translate between the two by composing or decomposing relations. This translation
Optimal and Suboptimal Singleton Arc Consistency Algorithms
- Professional Book Center
, 2005
"... Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent af-ter the assignment of a value to a variable. Algo-rithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give ..."
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Cited by 40 (4 self)
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Singleton arc consistency (SAC) enhances the pruning capability of arc consistency by ensuring that the network cannot become arc inconsistent af-ter the assignment of a value to a variable. Algo-rithms have already been proposed to enforce SAC, but they are far from optimal time complexity. We give a lower bound to the time complexity of en-forcing SAC, and we propose an algorithm that achieves this complexity, thus being optimal. How-ever, it can be costly in space on large problems. We then propose another SAC algorithm that trades time optimality for a better space complexity. Nev-ertheless, this last algorithm has a better worst-case time complexity than previously published SAC al-gorithms. An experimental study shows the good performance of the new algorithms. 1
Permutation Problems and Channelling Constraints
- TR 26, APES Group
, 2001
"... When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual ..."
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Cited by 39 (2 self)
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When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual representation. In the dual representation, dual variables stand for the primal values, whilst dual values stand for the primal variables. By means of channelling constraints, a combined model can have both primal and dual variables. In this paper, we perform an extensive theoretical and empirical study of these different models. Our results will aid constraint programmers to choose a model for a permutation problem. They also illustrate a general methodology for comparing different constraint models.
Dual Modelling of Permutation and Injection Problems
- Journal of Artificial Intelligence Research
, 2004
"... When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many ..."
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Cited by 30 (8 self)
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When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. Consider, for example, permutation problems in which we have as many values as variables, and each variable takes an unique value. In such problems, we can choose between a primal and a dual viewpoint. In the dual viewpoint, each dual variable represents one of the primal values, whilst each dual value represents one of the primal variables. Alternatively, by means of channelling constraints to link the primal and dual variables, we can have a combined model with both sets of variables. In this paper, we perform an extensive theoretical and empirical study of such primal, dual and combined models for two classes of problems: permutation problems and injection problems. Our results show that it often be advantageous to use multiple viewpoints, and to have constraints which channel between them to maintain consistency. They also illustrate a general...
Theoretical analysis of singleton arc consistency
- Proceedings ECAI’04 Workshop on Modelling and solving problems with constraints
, 2004
"... Singleton arc consistency (SAC) is a consistency property that is simple to specify and is stronger than arc consistency. Algorithms have already been proposed to enforce SAC, but they have a high time complexity. In this paper, we give a lower bound to the worst-case time complexity of enforcing SA ..."
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Cited by 28 (3 self)
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Singleton arc consistency (SAC) is a consistency property that is simple to specify and is stronger than arc consistency. Algorithms have already been proposed to enforce SAC, but they have a high time complexity. In this paper, we give a lower bound to the worst-case time complexity of enforcing SAC on binary constraints. We discuss two interesting features of SAC. The first feature leads us to propose an algorithm for SAC that has optimal time complexity when restricted to binary constraints. The second feature leads us to extend SAC to a stronger level of local consistency that we call Bidirectional SAC (BiSAC). We also show the relationship between SAC and the propagation of disjunctive constraints. 1
A greedy approach to establish singleton arc consistency
- In Proceedings of IJCAI’05
, 2005
"... In this paper, we propose a new approach to establish Singleton Arc Consistency (SAC) on constraint networks. While the principle of existing SAC algorithms involves performing a breadth-first search up to a depth equal to 1, the principle of the two algorithms introduced in this paper involves perf ..."
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Cited by 26 (12 self)
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In this paper, we propose a new approach to establish Singleton Arc Consistency (SAC) on constraint networks. While the principle of existing SAC algorithms involves performing a breadth-first search up to a depth equal to 1, the principle of the two algorithms introduced in this paper involves performing several runs of a greedy search (where at each step, arc consistency is maintained). It is then an original illustration of applying inference (i.e. establishing singleton arc consistency) by search. Using a greedy search allows benefiting from the incrementality of arc consistency, learning relevant information from conflicts and, potentially finding solution(s) during the inference process. Furthermore, both space and time complexities are quite competitive. 1
Fast Optimal Instruction Scheduling for Single-issue Processors with Arbitrary Latencies
, 2001
"... Instruction scheduling is one of the most important steps for improving the performance of object code produced by a compiler. The local instruction scheduling problem is to find a minimum length instruction schedule for a basic block subject to precedence, latency, and resource constraints. In ..."
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Cited by 25 (8 self)
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Instruction scheduling is one of the most important steps for improving the performance of object code produced by a compiler. The local instruction scheduling problem is to find a minimum length instruction schedule for a basic block subject to precedence, latency, and resource constraints. In this paper we consider local instruction scheduling for single-issue processors with arbitrary latencies. The problem is considered intractable, and heuristic approaches are currently used in production compilers. In contrast, we present a relatively simple approach to instruction scheduling based on constraint programming which is fast and optimal. The proposed approach uses an improved constraint model which allows it to scale up to very large, real problems. We describe powerful redundant constraints that allow a standard constraint solver to solve these scheduling problems in an almost backtrack-free manner. The redundant constraints are lower bounds on selected sub-problems which take advantage of the structure inherent in the problems. Under specified conditions, these constraints are sometimes further improved by testing the consistency of a sub-problem using a fast test. We experimentally evaluated our approach by integrating it into the Gnu Compiler Collection (GCC) and then applying it to the SPEC95 floating point benchmarks. All 7402 of the benchmarks' basic-blocks were optimally scheduled, including basic-blocks with up to 1000 instructions. Our results compare favorably to the best previous approach which is based on integer linear programming (Wilken et al., 2000): Across the same benchmarks, the total optimal scheduling time for their approach is 98 seconds while the total time for our approach is less than 5 seconds. 1
Trying Again to Fail-First
- In: Recent Advances in Constraints. Papers from the 2004 ERCIM/CologNet Workshop-CSCLP 2004. LNAI No. 3419
, 2005
"... In ECAI 1998 Smith & Grant performed a study [1] of the fail-first principle of Haralick & Elliott [2]. The fail-first principle states that "To succeed, try first where you are most likely to fail." For constraint satisfaction problems (CSPs), Haralick & Elliott realized th ..."
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Cited by 22 (7 self)
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In ECAI 1998 Smith & Grant performed a study [1] of the fail-first principle of Haralick & Elliott [2]. The fail-first principle states that "To succeed, try first where you are most likely to fail." For constraint satisfaction problems (CSPs), Haralick & Elliott realized this principle by minimizing branch depth.
